Optimal allocation of a fixed production under price uncertainty

Abstract

In this paper, we consider a model of production allocation in the context of the theory of the firm under uncertainty. This is the case of a firm that has just produced a known amount of an output and can allocate it to two possible ends: one with a certain price, the other with an uncertain price. We first establish conditions to determine whether the firm will make use of both ends or of only one of them. In particular, we find a limit value for the certain price (which we call the frontier price) below which the firm decides to allocate the total amount of production to the uncertain end. We then study comparative-static effects on the optimal output allocated to each end, and also on the frontier price. Finally, we analyze an application concerning the middleman who buys the firm's output in the certain end. This is a pricing problem: namely obtaining the price in the certain end that the middleman must offer to the producer in order to attain a desired amount of output. In two specific cases, we also provide closed-form expressions for the optimal allocation to both ends and for the frontier price.

Sourcing decision under interconnected risks: an application of mean–variance preferences approach

“…Following this we have categorized the sources of risks into three types: viz., demand side risks, supply side risks, and background risks. Considering these three types of risks, several authors (e.g., Kumbhakar & Tsionas, 2010;Rodríguez-Puerta & Álvarez-López, 2016) have evaluated the optimal choice of a decision maker in the presence of either demand-or supply-side risks. For instance, Kumbhakar and Tsionas (2010) considered von Neumann-Morgenstern (hereafter vNM) expected utility (hereafter EU) approach to analyse only supply-side risk for a risk averse manufacturer.…”

“…For instance, Kumbhakar and Tsionas (2010) considered von Neumann-Morgenstern (hereafter vNM) expected utility (hereafter EU) approach to analyse only supply-side risk for a risk averse manufacturer. Rodríguez-Puerta and Álvarez-López (2016), on the other hand, in an EU framework, have considered only demand-side risk to decide optimal production allocation of a fixed amount of output to the two possible destinations: one with certain price and another with uncertain price. However, due to the inherent complexity of the classical EU models, it is almost impossible to analyse the implications of changes in dependence structure or interconnectedness among multiple risks on the risk preference pattern driving the optimal sourcing decision within a SC network system.…”